1. So far we are familiar with three atomic Models. The first was that of

Democritus (460-370) BC, the ancient Greek philosopher, who proposed

that the smallest unit  of matter was a small, single, indivisible particle,

"atomos."

2. This belief lasted for almost 2300 years, until the 1890's when the

British Physicist, J. J. Thomson discovered the electron using his CRT.

His model was known as the "Plum Pudding" Model.

3. In the early 1900's, Ernest Rutherford, also from England proposed his

Planetary Model, based on his "Gold Foil" Experiment. This atomic model

was characterized as mostly empty space, but with a very dense, positively

charged nucleus, and orbiting electrons.

4. While the Rutherford (Planetary) model focused on describing the nucleus,

the electron was depicted as an orbiting planet. The flaw with the planet-like

model is that an electron particle moving in a circular path would be

accelerating. 

5. An accelerating electron creates a changing magnetic field. This changing

magnetic field would carry energy away from the electron, eventually slowing

it down and allowing it to be "captured" by the nucleus.

6. In 1913, the Danish physicist Niels Bohr (1885-1962) managed to

explain the a new atomic model as an extension of Rutherford's

description of the atom.

7. Bohr agreed that the negatively charged electrons revolve about the

positively charged atomic nucleus because of the attractive electrostatic

force according to Coulomb's law.

8. But the electron can be taken not only as a particle, but also as a

de Broglie wave (wave of matter) which interferes with itself.

9. The orbit is only stable, if it meets the condition for a standing wave:

The circumference must be an integer multiple of the wavelength.

The consequence is that only special values of radius and energy are allowed.

10. According to classical electrodynamics, a charge, which is subject to

centripetal acceleration on a circular orbit, should continuously radiate

electromagnetic waves.

11. Thus, because of the loss of energy, the electron should spiral into the

nucleus very soon. By contrast, an electron in Bohr's model emits no energy,

as long as its energy has one of the above-mentioned values.

12. However, an electron which is not in the lowest energy level (n = 1), can

make a spontaneous change to a lower state and thereby emit the energy

difference in the form of a photon (particle of light).

13. By calculating the wavelengths of the corresponding electromagnetic

waves, one will get the same results as by measuring the lines of the

hydrogen spectrum.

14. We must not take the idea of electrons, orbiting around the atomic

nucleus, for reality. Bohr's model of the hydrogen atom was only an

intermediate step on the way to a precise theory of the atomic structure,

which was made possible by quantum mechanics and quantum

electrodynamics.

15. Still, the most important properties of atomic and molecular structure

may be exemplified using a simplified picture of an atom that is called the

Planetary Quantum or Bohr Model.

16. Again, this model was proposed by Niels Bohr in 1915 and although it

is not completely correct, but it has many features that are approximately

correct and it is sufficient for much of our discussion.

17. The correct theory of the atom is called Quantum Mechanics; the Bohr

Model is an approximation to quantum mechanics that has the virtue of

being much simpler to understand.

18. In the Bohr Model the neutrons and protons occupy a dense central

region called the nucleus, and the electrons orbit the nucleus much like

planets orbiting the Sun (but the orbits are not confined to a plane as is

approximately true in the Solar System).

19. This similarity between a Planetary Model and the Bohr Model of the

atom ultimately arises because the attractive gravitational force in a solar

system and the attractive Coulomb (electrical) force between the positively

charged nucleus and the negatively charged electrons in an atom are

mathematically of the same form.

20. The form is the same, but the intrinsic strength of the Coulomb interaction

is much larger than that of the gravitational interaction; in addition, there are

positive and negative electrical charges so the Coulomb interaction can be

either attractive or repulsive, but gravitation is always attractive in our present

Universe.

21. Based on the spectrum of atomic hydrogen and the fact that each gas has

a unique emission and absorption spectrum, Niels Bohr proposed his Quantum-

Mechanical Atomic Model instead of Rutherford's Planetary Model.

22. He proposed that electrons can move from one energy level to another by

absorbing or emitting photons. His equations were: (a) for orbital radii.

r_n = 5.3x10^-11 m x n² , and (b) for the ionization energy associated with each

level,E_n = -13.6 eV x 1/n² , with n = 1,2,3,... , the energy level number.

The electron-volt (eV) is the energy unit for electrons, 1 eV = 1.6x10^-19 J .

23. Werner Heisenberg (1901-1976) determined that it is not possible to know

the exact position and momentum of the electron, the Uncertainty Principle.

24. Arthur Holly Compton (1892-1962) bombarded a graphite block with X-rays

demonstrating the momentum of photons (The Compton Effect ). The equation

is mv = p = h/λ .

25. James Chadwick (1891-1974) an original member of Rutherford's research

team proved the existence of neutrons in 1932.

26. Light Amplification by Stimulated Emission of Radiation (LASER), which

was explained by Einstein in 1917, was invented in 1960. Laser light is very

directional, powerful, monochromatic, and coherent, making it very useful.

1. Henri Becquerel (1852-1908) accidentally found that all compounds

containing uranium emitted rays that penetrate and fog photographic plates,

after examining a mysterious rock.

2. Ernest Rutherford (1871-1937) identified alpha, beta, and gamma radiation

and used alpha particles to bombard gold foil. He found that most of an atom

is empty space but contains a massive positively charged nucleus.

3. The Curies, Pierre and Marie, were the first to discover other radioactive

elements, for example, Polonium and Radium.

4. The nucleus can be characterized by a mass number, A, an atomic number,

Z, and a neutron number, N, with A = Z + N. Atoms having the same number

of protons but different amounts of neutrons are called isotopes.

5. The nucleus of an atom contains most of the mass, consists of protons

and neutrons, with protons and neutrons termed as "nucleons."

6. We use the Atomic Mass Unit (amu), or u, for nucleon mass. To convert just

use the fact that 1 u = 1.6605x10^-27 kg. This means that we now have the

mass of a proton as, 1 p = 1.007825 u, and a neutron, 1 n = 1.008665 u.

7. The change, transmutation, in an atomic nucleus can be natural or artificial.

Enrico Fermi (1901-1954) successfully produced artificially radioactive elements

in the laboratory.

8. Radioactive decay produces three kinds of particles: alpha, α, helium nuclei;

beta, β, high-speed electrons; and gamma, γ, ray photons.

9. Bombardment of nuclei by protons, neutrons, alpha particles, electrons,

gamma rays, or other nuclei can produce a nuclear reaction.

10. Linear accelerators, synchrotrons, and super-colliders produce high-energy

protons and electrons which can collide with each other or an atomic nucleus.

11. Particle detectors include photographic plates, the Geiger-Muller tube,

scintillation screens, and the cloud chamber.

12. Alpha can be stopped by thick paper, beta by thick aluminum foil, and a

few centimeters of lead will stop gamma.

13. During positron decay a proton changes into a neutron with the emission

of a positron and a neutrino.

14. When matter and antimatter combine, all matter is converted into energy,

or lighter matter-antimatter particle pairs. By pair production, energy is

converted into a matter-antimatter particle pair.

15. The weak interaction operates in beta decay while the strong force binds

the nucleus together. During beta decay a neutron changes into a proton and

the nucleus emits a beta particle and a mass-less antineutrino.

16. The binding energy is the energy equivalent of the mass defect. The

assembled nucleus has less mass than its constituent parts due to mass-to-

energy conversion, Binding Energy = (Δm)c² , with Δm as the mass defect.

17. Nuclear reactors use the energy released in fission as heat to boil water,

which produces steam, that turns turbine blades to run a generator.

18. The binding energy of the nucleus is the difference in energy between its

nucleons when bound and its nucleons when unbound. Energy-mass equivalence

can be computed using 1 amu = 931 MeV.

19. The half-life, T_½ , is the time required for half the original nuclei of a

radioactive substance to undergo radioactive decay. We use the equation

A = A₀∙2^-n where n is the number of half-lives, and A indicating amount.

20. The decay constant, lambda, λ, indicates the rate of radioactive decay.

Half-life can also be calculated by T_½ = .693/λ .

21. Nuclear reactions involve a change in the nucleus and can be given by

equations. In equations for nuclear reactions, subscripts and superscripts must

agree on both sides.

22. In a nuclear equation the sums of the subscripts (atomic number or particle

charge) on both sides of the equation are equal and the sums of the superscripts

(mass number) on both sides of the equation are equal.

23. In fission, heavier nuclei split to form lighter nuclei and energy is released.

In fusion, lighter nuclei combine to form heavier nuclei with more binding energy.

1. Chemistry can be understood in the physics of 3 particles (proton, neutron

and electron), and the influence of the electromagnetic force.

6. The Standard Model is conceptually simple and contains a description of the

elementary particles and forces. The SM particles are the 6 quarks, which include

the up and down quarks that make up the neutron and proton.

7. The 6 leptons include the electron and its partner, the electron neutrino. The 4

bosons are particles that transmit forces and include the photon, which transmits

the electromagnetic force. Click HERE for Force descriptions.

8. With the observation of the tau neutrino at Fermilab, all 12 fermions and all 4

gauge bosons have been observed. Seven of these 16 particles (charm, bottom,

top, tau neutrino, W, Z, gluon) were predicted by the Standard Model before

they were observed experimentally!  

9. There is one additional particle predicted by the Standard Model called the

Higgs, which has not yet been observed. It is needed in the model to give mass

to the W and Z bosons, consistent with experimental observations.

10. While photons and gluons have no mass, the W and Z are quite heavy.

The W weighs 80.3 GeV (80 times as much as the proton) and the Z weighs

91.2 GeV.

11. The Higgs is expected to be heavy as well. Direct searches for it at CERN

dictate that it must be heavier than 110 GeV.

And to get full credit for homework make sure you follow these steps:

(i) read the problem and identify the given variables

(ii) determine what you are asked to solve for

(iii) find the correct formula to use

(iv) use algebra to isolate the unknown

(v) substitute-in the given information and simplify.

View the NEW PowerPoint™Slides.

Problem Set #1.

Problem Set #2 (Test Review).